Modeling the Impact of Proactive Community Case Management on Reducing Confirmed Malaria Cases in Sub-Saharan African Countries

ABSTRACT. Malaria continues to be a major source of morbidity and mortality in sub-Saharan Africa. Timely, accurate, and effective case management is critical to malaria control. Proactive community case management (ProCCM) is a new strategy in which a community health worker “sweeps” a village, visiting households at defined intervals to proactively provide diagnostic testing and treatment if indicated. Pilot experiments have shown the potential of ProCCM for controlling malaria transmission; identifying the best strategy for administering ProCCM in terms of interval timings and number of sweeps could lead to further reductions in malaria infections. We developed an agent-based simulation to model malaria transmission and the impact of various ProCCM strategies. The model was validated using symptomatic prevalence data from a ProCCM pilot study in Senegal. Various ProCCM strategies were tested to evaluate the potential for reducing parasitologically confirmed symptomatic malaria cases in the Senegal setting. We found that weekly ProCCM sweeps during a 21-week transmission season could reduce cases by 36.3% per year compared with no sweeps. Alternatively, two initial fortnightly sweeps, seven weekly sweeps, and finally four fortnightly sweeps (13 sweeps total) could reduce confirmed malaria cases by 30.5% per year while reducing the number of diagnostic tests and corresponding costs by about 33%. Under a highly seasonal transmission setting, starting the sweeps early with longer duration and higher frequency would increase the impact of ProCCM, though with diminishing returns. The model is flexible and allows decision-makers to evaluate implementation strategies incorporating sweep frequency, time of year, and available budget.

Natural Death rate 5.9/1000 ppl per year 5.9/1000 ppl per year

1: Simulation Model of the Mosquito Population
To model the dynamics of the mosquito population, we use the general framework proposed in Cailly et al. 6 for Anopheles, and Tran at al 7 for Aedes albopictus.Table S2 and Figure S2 depict the stages in the life cycle of mosquitos: aquatic stages (E, eggs; L, Larvae; P, pupae), emerging adult stage (A em ), nulliparous stages (A 1h , A 1g , A 1o ) and parous stages (A 2h ,  2 ,  2 ).Note that only the female mosquitoes are represented in the adult stage.Host-seeking nulliparous A 1 Nulliparous engorged A 1 Nulliparous seeking oviposition sites A 2h Host-seeking parous A 2g Parous engorged A 2 Parous seeking oviposition sites The duration of each stage in the mosquito life cycle depends on several factors, such as temperature and water availability (precipitation).Temperature impacts the mortality and transition rates of larvae, pupae and adults, while precipitation impacts the environment's carry capacity of aquatic stages, increasing the number of breeding sites available for mosquitos.For example, the climate in Senegal is tropical with high temperatures all year round and rainy season from May through November.The high transmission season starts in early July and ends in late October.We divide a year into favorable season and diapause period, where eggs stop hatching until the next favorable season when they hatch if they are immerged in water.
The mosquito population dynamic model is based on a system of ordinary differential equations (Equation (1)); these equations model how the mosquito population behaves over time, taking into account factors such as mortality rates at different stages and the temperature required for egg development.The parameters and functions are defined in Table S3 and Table S4.The adult female mosquito population (  ) is divided into three groups: uninfected mosquitos (  ), infected but not yet infectious mosquitos (  ), and infectious mosquitos (  ), i.e.,   =   +   +   .T(t) and P(t) represent the daily mean temperature in Celsius and precipitation in millimeters, respectively, on day t.P norm () is defined as the rainfall amount summed over a two week period and normalized afterwards.
where z = 0 during diapause and 1 otherwise.A human infection begins with a successful contact by an infectious mosquito.In an infected human body, the malaria parasite undergoes a pre-erythrocytic liver stage first, which typically lasts for 1-2 weeks, before the onset of the blood stage.During the blood stage, the sexual form of the malaria parasite, the gametocyte, is produced and thus the infected human becomes infectious to mosquitoes 10 .The duration from a human being infected by a mosquito to him/her being infectious to mosquitoes is defined as the incubation period.
After a successful infection by a mosquito, the infected human also goes through (some of) the following phases, based on the severity of their symptoms: An infected human first goes through asymptomatic parasitemia phase ( ℎ ), which lasts between 6 to 14 days 12 , in which there are no symptoms.After this, he/she begins to show mild (uncomplicated) illness symptoms, including fever, chills, headaches, diaphoresis, etc.If not actively seeking treatment, a human in the uncomplicated illness phase could go into the severe malaria phase after 5-7 days for adults and 1-2 days for children under 5, as the parasite density accumulates within his/her body 10 .Since the duration of the incubation state doesn't necessarily coincide with the asymptomatic parasitemia phase, an infected human can become infectious either at the end of the asymptomatic parasitemia phase or at the beginning of the uncomplicated illness phase.
We further differentiate the level of human infectiousness depending on where a human is among the phases of the infected state.As gametocytes in P. falciparum infections arise from asexual parasites (i.e., merozoites), there could be a positive correlation between the density of asexual and sexual parasite (gametocytes) 2 .In nonimmune individuals, hyperparasitemia (>5% parasitemia or >250 000 parasites/ul) is generally associated with severe disease 12 .Research also suggests that the level of infectiousness of a human is a concave increasing function of female gametocyte density 13 .Thus, we assume that the human level of infectiousness, i H , linearly increases from 0 to 1 during the uncomplicated illness phase, i.e., where t is how long an infected human has been in the uncomplicated illness phase, and T in is the total duration of the uncomplicated illness phase.The human's infectiousness level is highest, i.e., i H = 1, during the severe malaria phase.State and transition parameters for the human infection dynamic model are provided in Tables S5-S7.

States Explanation Duration [Day]


Notes & References
T

Section 2.3 Interaction between Human and Mosquito Populations
An uninfected clean non-immune human is susceptible to malaria and could be infected (with probability   ) after a bite from an infectious mosquito.We assume that every human has equal chance of being contacted by any mosquito 24 and children under 5 years old do not have immunity and thus, always show symptoms if infected (  = ) 22 .Although recent literature has shown that these assumptions are not quite realistic, particularly with regard to non-uniform infectivity 25,26 for simplicity of the hybrid model (which models mosquitos with simple Ordinary Differential Equations and humans with more complex agent-based models) we have let them stand in the current model, with the understanding that transmission results are not as conservative as they could be.
We adopt the idea of effective contact ratio that determines daily numbers of newly infected humans ( ℎ ) and newly infected mosquitos (  ) 27 and incorporate the individual infectiousness level, i H () ϵ [0,1].
The adjusted effective contact ratio equations are: where c v ,  ℎ are the successful biting rates, B(T) is the mosquito biting rate determined by mean daily temperature,  ℎ is the total number of humans in certain age group,   is the individual infectiousness level and   is the total number of humans in a certain infectious condition, e.g.   is the total number of infectious non-immune adults.Mandel et al. 18 and Filipe et al. 28 report values for successful biting rates in the range 0.2-0.5, but do not distinguish if humans are immune or naïve.The parameter values we have chosen are an educated guess based on these references and the fact that, because humans are immune or naïve (for which we use the higher 0.5 value), we are using the lower end of the range.

Section 2.4 Treatment and Residual Parasitemia
A human with uncomplicated malaria or severe malaria has the possibilities of "self-recovering", e.g., selftreatment, seeing a traditional healer, taking herbal medication 19 or simply recovering as the immune system responds, although the chance is small in the case of severe malaria.If a symptomatic human seeks treatment, at any stage after developing symptoms, we assume that he/she will receive artemisinin-based combination treatments (ACTs) for 3 days 10 , and the recovery process starts immediately after the first day 29 .Thus, the human infectiousness level would stop increasing as soon as the treatment begins.
Possibilities of treatment failure (  ) and mortality depends on the how long one has been infected as well as the severity of his/her symptoms.After the completion of treatment, some humans (50%) would be parasite free and the others would have residual parasitemia 31 .Humans with residual parasitemia have higher gametocyte density after treatments, and longer gametocyte carriage durations compared with those who are parasite free after ACTs 14 .In this model we assume that, after ACTs, a human preserves 50% to 75% of the infectiousness before treatment, and this level linearly decreases until the end of gametocyte carriage duration.

Section 2.5 Acquired Immunity against Malaria
After recovery, a non-immune human can gain immunity with a certain probability (  ) 22 .An immune human will become infected after a successful bite from an infected mosquito with a smaller chance 16 .After being infected, the immune human will then go through the asymptomatic parasitemia phase with a longer duration 30 .It is shown that with immunity, parasite density within an infected human body would be lower.
Thus, an immune human with asymptomatic parasitemia will have a much smaller possibility of showing symptoms, move to the uncomplicated malaria phase, and will be extremely unlikely to eventually progress into the severe malaria phase 2 .The majority of the immune humans with asymptomatic parasitemia will self-recover.Some who develop symptoms after the asymptomatic parasitemia phase may recover if they seek treatments.Losing immunity after recovery (  ) is also very unlikely under consistent heavy malaria exposure 27 .
Newborns begin their lives as uninfected non-immune humans.All humans are susceptible to natural death at a fixed rate.Traditionally, an infected human would only actively seek treatment (   ) if he/she developed symptoms.Treatment-seeking possibilities are different between humans in the adult group and children.Those who don't seek treatment will keep infecting uninfected mosquitos.ProCCM could actively detect infected humans with symptoms, give them treatments and terminate the infection loop.
All the states are listed in Table S5.The duration range for each state is adopted from corresponding literature.We assume that all distributions are uniform within the given ranges.The transition diagram for our human infection model is shown in Figure S4.

Figure S4 Human infection transition graph representing the stages, and transitions between stages, of human infections.
The parameters used in this simulation model are listed in Table S6 and Table S7.

Section 3. Model Validation, Experimental Results, and Sensitivity Analysis
In Linn et al., 4  In addition to validating our model with the number symptomatic infection cases and positive RDTs from the pilot study, we also compare with the Plasmodium falciparum parasite rate (PfPR).The yearly average PR 0−5 from our model is 9.3%, which lies in the published range. 31,32check that model sensitivities are roughly in keeping with expectations, we performed some trade-offs on ProCCM sweep coverage and simulation year.We adjusted the coverage from 80% to 95% while adopting weekly sweep strategy (C) and alternative strategy (I); the results are shown in Table S9 and Table S10.Since the weekly sweep strategy (strategy C in Table S8) provides higher frequency interventions, the results (number of malaria infection cases) are more sensitive to coverage change.
Decreasing coverage from 100% to 80% would result in 8.7% more infection cases per year.When adopting a strategy with lower intervention frequency (strategy I in Table S8), 6.3% more infection cases result per year.
We repeated the simulation from 2010 to 2013 when adopting the following strategies: i) no sweeps conducted, ii) weekly sweeps conducted during transmission season and iii) alternative strategy (I) conducted.We compared the total number of symptomatic malaria infection cases per year in Table S11.
The results show consistency from year to year: i) the total number of symptomatic infection cases per year is around 3700 in sweep strategy A (i.e., comparison group); ii) conducting weekly sweeps could reduce 31% to 36% of year-round infection cases; iii) conducting alternative strategy (I) could reduce 27% to 31% of year-round infection cases, while reducing 33% of the implementation cost.For most of the sub-Sahara African countries, funding for malaria intervention is a major barrier.Thus, we aim at exploring a better option that is more cost-efficient while providing promising results in infection control.Assuming each sweep has the same coverage, with the same amount of homecare providers, the average number of malaria infection cases identified per sweep would be an essential indicator of the cost efficiency for ProCCM strategies.Obviously, to not implement ProCCM at all would not induce any cost.
ProCCM sweeps started on July 8th and ended on Nov 25 th of 2013 in the pilot study.To find the optimal starting date of sweeps, we first proposed 13 sweep strategies, all of which are composed of 7 consecutive weekly strategies and each of them starting on a different week during peak season; results of this analysis are reported in Table S12.We only selected 7 out of 21 sweeps in this comparison set to reduce the cost of intervention.By exhaustive search, we identified the optimal strategy with the current constraints: strategy G test case #1 which starts on the 27th week and lasts until the end of the 32nd week.
With 26.4% reduction in infection cases, it is still not comparable to having 21 weekly sweeps, but twothirds of the cost is reduced.We repeated the analysis on years 2010, 2011 and 2012.In all three cases, the optimal starting weeks for 7 consecutive weekly sweeps are week 27, corresponding to strategy G.
Strategy G test cases #5 to #13 are shown to be ineffective compared to strategy B, where only three sweeps are adopted.Since the peak of malaria prevalence is reached at the mid-late peak season, starting intervention during mid-peak season is not effective when the malaria prevalence within the mosquito population is already very high.Early intervention is needed for effective malaria control.More details about yearly number of symptomatic and asymptomatic cases of all ages and max prevalence for this weekly sweeps strategy can be found in Figures S5-S7.S13).In all four cases, the optimal starting week for 7 consecutive biweekly sweeps is at the beginning of peak season on week 27, corresponding to strategy test case H.The weekly and biweekly strategies with only 7 sweeps perform comparably in terms of outcomes, but higher frequency, especially at the beginning of the transmission season, is preferred.More details about yearly number of symptomatic and asymptomatic cases of all ages and max prevalence for this biweekly sweeps strategy can be found in Figures S8 -S10.

Section 4. Limitations
There are parameters in our human infection transition model that are estimated within certain published ranges.We adopted parameters that fit our model the best and provided the closest result to existing data in Linn et al 4 .To test the robustness of our conclusions, we chose varying values of environment carrying capacity and reran the simulation.As shown in Table S14, despite different environment capacities and the resulting reductions of symptomatic cases per year, strategy I is at least as effective as strategy C while reducing the number of sweeps.
This robustness test can be regarded as a thumbnail of the large-scale experiment involving other parameters.Different parameters lead to different transmission intensity, which can be measured by entomological inoculation rate (EIR), as shown in Table S15.Within a certain range of transmission intensity, strategy I highlights its advantage in balancing resources and effectiveness.

FigureSection 2
Figure S1 Temperature and precipitation data in Senegal from 2010 to 2013 Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

Figure
Figure S2 Mosquito population dynamic model representing the stages, and transitions between stages, in the life cycle of mosquitos.

Figure
Figure S13 Rolling mean of symptomatic cases for Strategy C (i.e., weekly sweeps) for simulation iterations up to 50.

Figure
Figure S14 Rolling standard deviation of symptomatic cases for Strategy C (i.e., weekly sweeps) for simulation iterations up to 50.

Table S1
Human characteristics data for the simulation model

Section 2.2. Model Parameters for Human Infection
Jan FebMar Apr May Jun Jul Aug Sep Oct Nov Dec Jan FebMar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan FebMar Apr May Jun Jul Aug Sep Oct Nov Dec k  () =   (  () + 1) B(T(t)) Mosquito biting rate (day -1 ) 0.000203T(t)(T(t) − 11.7)√(42.3− T(t)) 1,669 symptomatic infection cases are documented in the pilot intervention group from The symptomatic infection cases reported in Table S8 (0.496*4747=2,354) lies in the range of year-round infection cases.Moreover, the total number of positive RDTs given during sweeps reported in Linn et al. is 647.The estimated number of positive RDTs in the comparison group after adjustment is 933, which lies in the 95% confidence interval of our results.
Our simulation results show that about 90% of the infection cases occurred during peak season.Considering this, the estimated range for year-round infection cases is[2338, 2,454].

Table S11 Total
Infections for Strategies A, C, and I in multiple years.

Table S12
Next, we examined the effect of having a longer intervention period by using biweekly sweeps.Strategy E conducts 11 biweekly sweeps converging with the same 21-week period starting on July 8th.The biweekly strategy could reduce the cost by half while still following the requirement of an early start and long duration.Alternatively, Strategy D conducts 21 weekly sweeps but each time only having 50% population coverage instead of 100%.Reduction in malaria infections in both cases are similar, with strategy D performing slightly better.Under Strategy D, there are infectious humans who were detected earlier than under the biweekly sweeps due to randomness.Theoretically having 50% coverage each sweep could also reduce the cost by half, yet the idea of randomly selecting 50% of the symptomatic humans to test is hard to implement.Covering half of the villages on odd weeks and the other half on even weeks in more likely to be carried out in practice.Without the randomness in the selection, the outcome is going to be different.Within the low-cost setting, we examined the optimal starting date for 7 consecutive biweekly sweeps in years 2010, 2011, 2012 and 2013 (results for year 2013 are reported in Table Simulation results for 7 consecutive weekly sweeps with different starting dates (variations to Strategy G)

Table S13
Simulation results for 7 consecutive biweekly sweeps with different starting dates (variations to Strategy H)Note that the simulation stabilizes after approximately 40 simulation replications; for example, the rolling mean and standard deviation of symptomatic cases for Strategy C (i.e., weekly sweeps) are shown in FiguresS13 and S14, respectively.
Figure S12The total number of symptomatic infection cases identified by ProCCM sweeps per year for Strategy C: weekly 335 sweeps, given variations in treatment seeking rates at mild condition and severe condition, respectively.The legend corresponds 336 to treatment seeking rates at severe condition.

Table S14 Mean
Reduction of symptomatic cases (from 0.0 to 1.0) per year (compared to A, no sweeps) for various strategies with different Larvae and pupae environment carrying capacity Table S15 Mean Daily EIR during the high transmission season for various strategies with different Larvae and pupae